TY - JOUR
A2 - Amelino-Camelia, Giovanni
AU - García-Compeán, H.
AU - Obregón, O.
AU - Santos-Silva, R.
PY - 2015
DA - 2015/10/19
TI - Towards Noncommutative Linking Numbers via the Seiberg-Witten Map
SP - 845328
VL - 2015
AB - Some geometric and topological implications of noncommutative Wilson loops are explored via the Seiberg-Witten map. In the abelian Chern-Simons theory on a three-dimensional manifold, it is shown that the effect of noncommutativity is the appearance of 6n new knots at the nth order of the Seiberg-Witten expansion. These knots are trivial homology cycles which are Poincaré dual to the higher-order Seiberg-Witten potentials. Moreover the linking number of a standard 1-cycle with the Poincaré dual of the gauge field is shown to be written as an expansion of the linking number of this 1-cycle with the Poincaré dual of the Seiberg-Witten gauge fields. In the process we explicitly compute the noncommutative “Jones-Witten” invariants up to first order in the noncommutative parameter. Finally in order to exhibit a physical example, we apply these ideas explicitly to the Aharonov-Bohm effect. It is explicitly displayed at first order in the noncommutative parameter; we also show the relation to the noncommutative Landau levels.
SN - 1687-9120
UR - https://doi.org/10.1155/2015/845328
DO - 10.1155/2015/845328
JF - Advances in Mathematical Physics
PB - Hindawi Publishing Corporation
KW -
ER -